Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary

Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Diffusion MRI of Structural Brain Plasticity Induced by a Learning and Memory Task

Background: Activity-induced structural remodeling of dendritic spines and glial cells was recently proposed as an important factor in neuroplasticity and suggested to accompany the induction of long-term potentiation (LTP). Although T1 and diffusion MRI have been used to study structural changes resulting from long-term training, the cellular basis of the findings obtained and their relationship to neuroplasticity are poorly understood. Methodology/Principal Finding: Here we used diffusion tensor imaging (DTI) to examine the microstructural manifestations of neuroplasticity in rats that performed a spatial navigation task. We found that DTI can be used to define the selective localization of neuroplasticity induced by different tasks and that this process is age-dependent in cingulate cortex and corpus callosum and age-independent in the dentate gyrus. Conclusion/Significance: We relate the observed DTI changes to the structural plasticity that occurs in astrocytes and discuss the potential of MRI for probing structural neuroplasticity and hence indirectly localizing LTP

Differential Regulation of the Variations Induced by Environmental Richness in Adult Neurogenesis as a Function of Time: A Dual Birthdating Analysis

Adult hippocampal neurogenesis (AHN) augments after environmental enrichment (EE) and it has been related to some of the anxiolytic, antidepressant and neuroprotective effects of EE. Indeed, it has been suggested that EE specifically modulates hippocampal neurogenic cell populations over the course of time. Here we have used dual-birthdating to study two subpopulations of newborn neuron in mice (Mus musculus): those born at the beginning and at the end of enrichment. In this way, we demonstrate that while short-term cell survival is upregulated after an initial 1 week period of enrichment in 2 month old female mice, after long-term enrichment (2 months) neither cell proliferation nor the survival of the younger newly born cell populations are distinguishable from that observed in non-enriched control mice. In addition, we show that the survival of older newborn neurons alone (i.e. those born at the beginning of the enrichment) is higher than in controls, due to the significantly lower levels of cell death. Indeed, these parameters are rapidly adjusted to the sudden cessation of the EE conditions. These findings suggest both an early selective, long-lasting effect of EE on the neurons born in the initial stages of enrichment, and a quick response when the environment again becomes impoverished. Therefore, EE induces differential effects on distinct subpopulations of newborn neurons depending on the age of the immature cells and on the duration of the EE itself. The interaction of these two parameters constitutes a new, specific regulation of these neurogenic populations that might account for the long-term enrichment's behavioral effects

Absence of Ca2+-stimulated adenylyl cyclases leads to reduced synaptic plasticity and impaired experience-dependent fear memory

Ca2+-stimulated adenylyl cyclase (AC) 1 and 8 are two genes that have been shown to play critical roles in fear memory. AC1 and AC8 couple neuronal activity and intracellular Ca2+ increases to the production of cyclic adenosine monophosphate and are localized synaptically, suggesting that Ca2+-stimulated ACs may modulate synaptic plasticity. Here, we first established that Ca2+-stimulated ACs modulate protein markers of synaptic activity at baseline and after learning. Primary hippocampal cell cultures showed that AC1/AC8 double-knockout (DKO) mice have reduced SV2, a synaptic vesicle protein, abundance along their dendritic processes, and this reduction can be rescued through lentivirus delivery of AC8 to the DKO cells. Additionally, phospho-synapsin, a protein implicated in the regulation of neurotransmitter release at the synapse, is decreased in vivo 1 h after conditioned fear (CF) training in DKO mice. Importantly, additional experiments showed that long-term potentiation deficits present in DKO mice are rescued by acutely replacing AC8 in the forebrain, further supporting the idea that Ca2+-stimulated AC activity is a crucial modulator of synaptic plasticity. Previous studies have demonstrated that memory is continually modulated by gene–environment interactions. The last set of experiments evaluated the effects of knocking out AC1 and AC8 genes on experience-dependent changes in CF memory. We showed that the strength of CF memory in wild-type mice is determined by previous environment, minimal or enriched, whereas memory in DKO mice is unaffected. Thus, overall these results show that AC1 and AC8 modulate markers of synaptic activity and help integrate environmental information to modulate fear memory

Therapeutic Radionuclides: Making the Right Choice

Recently, there has been a resurgence of interest in nuclear medicine therapeutic procedures. Using unsealed sources for therapy is not a new concept; it has been around since the beginnings of nuclear medicine. Treatment of thyroid disorders with radioiodine is a classic example. The availability of radionuclides with suitable therapeutic properties for specific applications, as well as methods for their selective targeting to diseased tissue have, however, remained the main obstacles for therapy to assume a more widespread role in nuclear medicine. Nonetheless, a number of new techniques that have recently emerged, (e.g., tumor therapy with radiolabeled monoclonal antibodies, treatment of metastatic bone pain, etc.) appear to have provided a substantial impetus to research on production of new therapeutic radionuclides. Although there are a number of new therapeutic approaches requiring specific radionuclides, only selected broad areas will be used as examples in this article

Selective Survival and Maturation of Adult-Born Dentate Granule Cells Expressing the Immediate Early Gene Arc/Arg3.1

Progenitor cells in the adult dentate gyrus provide a constant supply of neuronal precursors, yet only a small fraction of these cells survive and develop into mature dentate granule cells (DGCs). A major challenge of current research is thus to understand the stringent selection process that governs the maturation and functional integration of adult-born DGCs. In mature DGCs, high-frequency stimulation (HFS) of the perforant path input elicits robust expression of the immediate early gene Arc/Arg3.1, trafficking of its mRNA to dendrites, and local synthesis of the protein necessary for consolidation of long-term potentiation (LTP). Given the synaptic commitment inherent in LTP consolidation, we considered that HFS-evoked expression of Arc could be used to timemap the functional integration of newborn DGCs. Dividing cells were birthmarked by BrdU-labeling at 1, 7, 14, 21, or 28 days prior to induction of LTP and expression of Arc was examined by confocal microscopy. Contrary to expectation, LTP did not induce Arc expression in newborn cells at any age, suggesting they might be refractory to synaptically-evoked Arc expression for at least one month. Importantly, however, spontaneous expression of Arc was detected in BrdU-labeled cells and strongly associated with the survival and maturation of NeuN-positive DGCs. Moreover, Arc expression at the earliest ages (1 and 7 days), clearly precedes the formation of glutamatergic synapses on new neurons. These results suggest an unexpected early role for Arc in adult-born DGCs, distinct from its functions in LTP, LTD, and homeostatic synaptic plasticity